Previously, we model all the 8 help indicators together using a cross-sectional model. Now, we try to model the financial help from other 7 practical helps seperately.
The financial help part is parameterized as follows: \[
P(Y_{i,J+1}^{TP}\mid \boldsymbol{x}_i) = P(Y^{TP*}_{i,J+1}>0),\\
Y^{TP*}_{i,J+1} = \boldsymbol{u}_{tp}^T \boldsymbol{x}_i + \epsilon_i^{TP}
\] \[
\boldsymbol{u}_{tp} = (u^{tp}_1, \ldots, u^{tp}_K)\\
u^{tp}_k\sim N(0, \sigma_{u_{tp}}^2),\ \text{for}\ k=1,\ldots,K\\
\sigma_{u_{tp}}^2 \sim IG(1.5, 0.01)
\] Note that an intercept is included in \(\boldsymbol{u}_{tp}^T \boldsymbol{x}_i\). And inverse-gamma(1.5, 0.01) is choosen because we want variances prior to be non-informative and inverse-gamma(0.01, 0.01) does not work in empty model case.
library(jsem)
#> Loading required package: coda
#> jsem 0.1 using 3 threads (see ?getjsem_threads())
load("jags.rda")
aidrp_data_simple <- list(ytp=jags.data$ytp, yfp = jags.data$yfp, xi=xi.start,
female = jags.data$female,
distlong = jags.data$distlong,
age40 = jags.data$age40,
partner = jags.data$partner,
clt2 = jags.data$clt2,
c2to4 = jags.data$c2to4,
c5to10 = jags.data$c5to10,
c11to16 = jags.data$c11to16,
cgt16 = jags.data$cgt16,
jbs3 = jags.data$jbs == 3,
jbs4 = jags.data$jbs == 4,
page70 = jags.data$page70,
plive = jags.data$plive %in% c(3, 4, 5, 7, 9))
dylanie_empty_res <- dylanie_model_fin_sep_simple(~1, data=aidrp_data_simple,
mcmc_len = 7500, verbose = T)
round(dylanie_sep_fin_summary(dylanie_empty_res, burnin = 2500)$statistics,2)
dylanie_full_res <- dylanie_model_fin_sep_simple(~female + distlong + age40 + partner +
clt2 + c2to4 + c5to10 + c11to16 +
cgt16 + jbs3 + jbs4 + page70 + plive,
data=aidrp_data_simple,
mcmc_len = 7500, verbose = T)
round(dylanie_sep_fin_summary(dylanie_full_res, burnin = 2500)$statistics,2)
| Mean | SD | Naive.SE | Time.series.SE | |
|---|---|---|---|---|
| g[1,1] | 0.00 | 0.00 | 0.00 | 0.00 |
| g[1,2] | 0.03 | 0.11 | 0.00 | 0.01 |
| g[1,3] | -0.37 | 0.20 | 0.00 | 0.04 |
| g[1,4] | 1.62 | 0.08 | 0.00 | 0.01 |
| b_tp[1] | -1.96 | 0.06 | 0.00 | 0.01 |
| b_fp[1] | -4.88 | 0.07 | 0.00 | 0.01 |
| u_tp[1] | -2.70 | 0.03 | 0.00 | 0.00 |
| u_fp[1] | -1.90 | 0.02 | 0.00 | 0.00 |
| sig2_tp | 2.91 | 0.13 | 0.00 | 0.02 |
| sig2_fp | 3.69 | 0.17 | 0.00 | 0.02 |
| sig2_u_tp | 3.69 | 7.42 | 0.10 | 0.10 |
| sig2_u_fp | 1.75 | 2.63 | 0.04 | 0.04 |
| rho | 0.23 | 0.03 | 0.00 | 0.00 |
| p[1] | 0.13 | 0.01 | 0.00 | 0.00 |
| p[2] | 0.13 | 0.01 | 0.00 | 0.00 |
| p[3] | 0.09 | 0.02 | 0.00 | 0.00 |
| p[4] | 0.65 | 0.02 | 0.00 | 0.00 |
| Mean | SD | Naive.SE | Time.series.SE | |
|---|---|---|---|---|
| b_tp_intercept | -2.27 | 0.07 | 0 | 0.01 |
| b_tp_female | 0.83 | 0.05 | 0 | 0.00 |
| b_tp_distlong | -0.82 | 0.07 | 0 | 0.01 |
| b_tp_age40 | 0.00 | 0.00 | 0 | 0.00 |
| b_tp_partner | -0.26 | 0.06 | 0 | 0.00 |
| b_tp_clt2 | -0.18 | 0.10 | 0 | 0.00 |
| b_tp_c2to4 | -0.23 | 0.08 | 0 | 0.00 |
| b_tp_c5to10 | 0.00 | 0.06 | 0 | 0.00 |
| b_tp_c11to16 | 0.06 | 0.06 | 0 | 0.00 |
| b_tp_cgt16 | 0.13 | 0.06 | 0 | 0.00 |
| b_tp_jbs3 | 0.38 | 0.13 | 0 | 0.01 |
| b_tp_jbs4 | 0.50 | 0.06 | 0 | 0.00 |
| b_tp_page70 | 0.03 | 0.00 | 0 | 0.00 |
| b_tp_plive | 0.58 | 0.05 | 0 | 0.00 |
| b_fp_intercept | -4.00 | 0.08 | 0 | 0.01 |
| b_fp_female | 0.75 | 0.06 | 0 | 0.00 |
| b_fp_distlong | -0.12 | 0.09 | 0 | 0.01 |
| b_fp_age40 | -0.05 | 0.01 | 0 | 0.00 |
| b_fp_partner | -0.64 | 0.07 | 0 | 0.00 |
| b_fp_clt2 | -0.19 | 0.08 | 0 | 0.00 |
| b_fp_c2to4 | -0.31 | 0.07 | 0 | 0.00 |
| b_fp_c5to10 | -0.13 | 0.06 | 0 | 0.00 |
| b_fp_c11to16 | -0.10 | 0.07 | 0 | 0.00 |
| b_fp_cgt16 | -0.09 | 0.11 | 0 | 0.01 |
| b_fp_jbs3 | 0.47 | 0.14 | 0 | 0.01 |
| b_fp_jbs4 | 0.26 | 0.08 | 0 | 0.00 |
| b_fp_page70 | 0.00 | 0.01 | 0 | 0.00 |
| b_fp_plive | -0.28 | 0.06 | 0 | 0.00 |
| u_tp_intercept | -2.90 | 0.10 | 0 | 0.01 |
| u_tp_female | -0.07 | 0.07 | 0 | 0.00 |
| u_tp_distlong | -0.13 | 0.08 | 0 | 0.00 |
| u_tp_age40 | 0.00 | 0.01 | 0 | 0.00 |
| u_tp_partner | -0.14 | 0.08 | 0 | 0.00 |
| u_tp_clt2 | 0.05 | 0.14 | 0 | 0.00 |
| u_tp_c2to4 | 0.00 | 0.11 | 0 | 0.00 |
| u_tp_c5to10 | 0.19 | 0.09 | 0 | 0.00 |
| u_tp_c11to16 | 0.00 | 0.09 | 0 | 0.00 |
| u_tp_cgt16 | 0.01 | 0.09 | 0 | 0.00 |
| u_tp_jbs3 | -0.07 | 0.18 | 0 | 0.00 |
| u_tp_jbs4 | -0.02 | 0.09 | 0 | 0.00 |
| u_tp_page70 | 0.01 | 0.01 | 0 | 0.00 |
| u_tp_plive | 0.65 | 0.07 | 0 | 0.00 |
| u_fp_ intercept | -1.54 | 0.06 | 0 | 0.00 |
| u_fp_ female | 0.19 | 0.05 | 0 | 0.00 |
| u_fp_ distlong | -0.25 | 0.06 | 0 | 0.00 |
| u_fp_ age40 | -0.07 | 0.00 | 0 | 0.00 |
| u_fp_ partner | -0.67 | 0.06 | 0 | 0.00 |
| u_fp_ clt2 | -0.06 | 0.09 | 0 | 0.00 |
| u_fp_ c2to4 | -0.06 | 0.07 | 0 | 0.00 |
| u_fp_ c5to10 | 0.12 | 0.06 | 0 | 0.00 |
| u_fp_ c11to16 | 0.14 | 0.06 | 0 | 0.00 |
| u_fp_ cgt16 | 0.01 | 0.08 | 0 | 0.00 |
| u_fp_ jbs3 | 0.28 | 0.11 | 0 | 0.00 |
| u_fp_ jbs4 | 0.16 | 0.06 | 0 | 0.00 |
| u_fp_ page70 | 0.02 | 0.00 | 0 | 0.00 |
| u_fp_ plive | 0.05 | 0.05 | 0 | 0.00 |
| sig2_tp | 1.99 | 0.08 | 0 | 0.01 |
| sig2_fp | 2.17 | 0.10 | 0 | 0.01 |
| sig2_u_tp | 0.75 | 0.33 | 0 | 0.01 |
| sig2_u_fp | 0.26 | 0.12 | 0 | 0.00 |
| rho | 0.49 | 0.02 | 0 | 0.00 |
| p[1] | 0.18 | 0.02 | 0 | 0.00 |
| p[2] | 0.11 | 0.02 | 0 | 0.00 |
| p[3] | 0.05 | 0.01 | 0 | 0.00 |
| p[4] | 0.67 | 0.03 | 0 | 0.00 |
partner has a coefficient of -0.14(0.08) for financial help, and -0.26(0.06) for practicle helps;plive has a coefficient of 0.65(0.07) for financial help, and a coefficient of 0.58(0.05) for practicle helps;female has a coefficient of 0.19(0.05) for financial help, and 0.75(0.06) for practicle helps;age40 has a coefficient of -0.07(0.00) for financial help, and -0.05(0.01) for practicle helps;partner has a coefficient of -0.67(0.06) for financial help, and -0.64(0.07) for practicle helps;There is no missing data for financial responses.
load("~/Dropbox/Projs/Files for Siliang/WP1 methods and analysis/jags.rda")
table(jags.data$ytp[,8])
##
## 0 1
## 13927 933
table(jags.data$yfp[,8])
##
## 0 1
## 12921 1939
We extend the previous parameterization of correlation between practical to/from parents helps as follows,
For \(i=1,...,N\), \[ \eta_i^{TP} = \boldsymbol{x}_i^T \boldsymbol{b}_{tp} + \epsilon_{i,1}\\ \eta_i^{FP} = \boldsymbol{x}_i^T \boldsymbol{b}_{fp} + \epsilon_{i,2}\\ \phi_i^{TP} = \boldsymbol{x}_i^T \boldsymbol{u}_{tp} + \epsilon_{i,3}\\ \phi_i^{FP} = \boldsymbol{x}_i^T \boldsymbol{u}_{fp} + \epsilon_{i,4}\\ \begin{bmatrix} \epsilon_{i,1}\\ \epsilon_{i,2}\\ \epsilon_{i,3}\\ \epsilon_{i,4} \end{bmatrix}\sim N\left( \boldsymbol{0}, \begin{bmatrix} \sigma_{tp}^2 & \rho_1\sigma_{tp}\sigma_{fp} & \rho_2\sigma_{tp} & \rho_3\sigma_{tp}\\ \rho_1\sigma_{tp}\sigma_{fp} & \sigma_{fp}^2 & \rho_4\sigma_{fp} & \rho_5\sigma_{fp}\\ \rho_2\sigma_{tp} & \rho_4\sigma_{fp} & 1 & \rho_6 \\ \rho_3\sigma_{tp} & \rho_5\sigma_{fp} & \rho_6 & 1 \end{bmatrix}\right),\\ \eta^{TP'}_i = \boldsymbol{x}_i^T\boldsymbol{b}_{tp} + \epsilon_{tp},\ \epsilon_{tp}\sim N(0, \sigma_{tp}^2),\\ \eta^{FP'}_i = \boldsymbol{x}_i^T\boldsymbol{b}_{fp} + \epsilon_{fp},\ \epsilon_{fp}\sim N(0, \sigma_{fp}^2) \]
And for \(i=1,...,N\), \[ P(Y^{TP}_{i,J+1}=1\mid \boldsymbol{x}_i) = P(\phi_i^{TP}>0)\\ P(Y^{FP}_{i,J+1}=1\mid \boldsymbol{x}_i) = P(\phi_i^{FP}>0) \]
Then for \(\xi_i=4\), \[ P(Y^{TP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic} (\alpha_j + \beta_j\eta^{TP}_i)\\ P(Y^{FP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic}(\alpha_j + \beta_j\eta^{FP}_i), \] For \(\xi_i=2\), \[ P(Y^{FP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic}(\alpha_j + \beta_j\eta^{FP'}_i) \] For \(\xi_i=3\), \[ P(Y^{TP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic}(\alpha_j + \beta_j\eta^{TP'}_i) \]
## Mean SD
## [1,] 0.48 0.02
## [2,] 0.61 0.02
## [3,] 0.32 0.02
## [4,] 0.20 0.03
## [5,] 0.57 0.02
## [6,] 0.02 0.02
b_tp
| Mean.old | Mean.new | SD.old | SD.new | |
|---|---|---|---|---|
| intercept | -2.35 | -2.81 | 0.06 | 0.08 |
| female | 0.84 | 0.84 | 0.05 | 0.05 |
| distlong | -1.09 | -0.90 | 0.07 | 0.08 |
| age40 | 0.00 | 0.00 | 0.00 | 0.00 |
| partner | -0.27 | -0.24 | 0.05 | 0.06 |
| clt2 | -0.14 | -0.23 | 0.09 | 0.08 |
| c2to4 | -0.21 | -0.19 | 0.08 | 0.07 |
| c5to10 | 0.04 | 0.02 | 0.06 | 0.06 |
| c11to16 | 0.05 | 0.04 | 0.06 | 0.07 |
| cgt16 | 0.12 | 0.14 | 0.06 | 0.06 |
| jbs3 | 0.35 | 0.36 | 0.13 | 0.12 |
| jbs4 | 0.45 | 0.52 | 0.06 | 0.07 |
| page70 | 0.03 | 0.04 | 0.00 | 0.00 |
| plive | 0.58 | 0.73 | 0.05 | 0.05 |
b_fp
| Mean.old | Mean.new | SD.old | SD.new | |
|---|---|---|---|---|
| intercept | -4.22 | -4.34 | 0.09 | 0.08 |
| female | 0.75 | 0.78 | 0.06 | 0.06 |
| distlong | -0.42 | -0.32 | 0.08 | 0.08 |
| age40 | -0.05 | -0.06 | 0.01 | 0.01 |
| partner | -0.67 | -0.74 | 0.07 | 0.07 |
| clt2 | -0.14 | -0.12 | 0.09 | 0.09 |
| c2to4 | -0.25 | -0.20 | 0.07 | 0.07 |
| c5to10 | -0.07 | -0.03 | 0.07 | 0.07 |
| c11to16 | -0.07 | -0.07 | 0.07 | 0.07 |
| cgt16 | -0.16 | -0.20 | 0.10 | 0.10 |
| jbs3 | 0.43 | 0.38 | 0.14 | 0.14 |
| jbs4 | 0.23 | 0.20 | 0.07 | 0.08 |
| page70 | 0.00 | 0.00 | 0.00 | 0.01 |
| plive | -0.34 | -0.32 | 0.06 | 0.06 |
| PTP.coef | FTP.coef | PTP.sd | FTP.sd | |
|---|---|---|---|---|
| intercept | -0.87 | -0.97 | 0.08 | 0.04 |
| female | 0.26 | -0.01 | 0.05 | 0.03 |
| distlong | -0.28 | -0.03 | 0.08 | 0.04 |
| age40 | 0.00 | 0.00 | 0.00 | 0.00 |
| partner | -0.07 | -0.03 | 0.06 | 0.04 |
| clt2 | -0.07 | 0.01 | 0.08 | 0.06 |
| c2to4 | -0.06 | 0.00 | 0.07 | 0.05 |
| c5to10 | 0.01 | 0.06 | 0.06 | 0.04 |
| c11to16 | 0.01 | 0.00 | 0.07 | 0.04 |
| cgt16 | 0.04 | 0.00 | 0.06 | 0.04 |
| jbs3 | 0.11 | -0.03 | 0.12 | 0.08 |
| jbs4 | 0.16 | -0.01 | 0.07 | 0.04 |
| page70 | 0.01 | 0.00 | 0.00 | 0.00 |
| plive | 0.22 | 0.21 | 0.05 | 0.03 |
| PFP.coef | FFP.coef | PFP.sd | FFP.sd | |
|---|---|---|---|---|
| intercept | -0.96 | -0.89 | 0.08 | 0.03 |
| female | 0.17 | 0.12 | 0.06 | 0.03 |
| distlong | -0.07 | -0.14 | 0.08 | 0.03 |
| age40 | -0.01 | -0.04 | 0.01 | 0.00 |
| partner | -0.16 | -0.35 | 0.07 | 0.03 |
| clt2 | -0.03 | -0.03 | 0.09 | 0.05 |
| c2to4 | -0.04 | -0.03 | 0.07 | 0.04 |
| c5to10 | -0.01 | 0.06 | 0.07 | 0.03 |
| c11to16 | -0.02 | 0.06 | 0.07 | 0.03 |
| cgt16 | -0.04 | 0.01 | 0.10 | 0.04 |
| jbs3 | 0.08 | 0.16 | 0.14 | 0.06 |
| jbs4 | 0.04 | 0.07 | 0.08 | 0.03 |
| page70 | 0.00 | 0.01 | 0.01 | 0.00 |
| plive | -0.07 | 0.05 | 0.06 | 0.03 |
b_tp
b_fp
u_tp